The use of prognostic scores for causal inference with general treatment regimes

In nonrandomised studies, inferring causal effects requires appropriate methods for addressing confounding bias. Although it is common to adopt propensity score analysis to this purpose, prognostic score analysis has recently been proposed as an alternative strategy. While both approaches were originally introduced to estimate causal effects for binary interventions, the theory of propensity score has since been extended to the case of general treatment regimes. Indeed, many treatments are not assigned in a binary fashion and require a certain extent of dosing. Hence, researchers may often be interested in estimating treatment effects across multiple exposures. To the best of our knowledge, the prognostic score analysis has not been yet generalised to this case. In this article, we describe the theory of prognostic scores for causal inference with general treatment regimes. Our methods can be applied to compare multiple treatments using nonrandomised data, a topic of great relevance in contemporary evaluations of clinical interventions. We propose estimators for the average treatment effects in different populations of interest, the validity of which is assessed through a series of simulations. Finally, we present an illustrative case in which we estimate the effect of the delay to Aspirin administration on a composite outcome of death or dependence at 6 months in stroke patients.

[1]  D. Rubin Estimating causal effects of treatments in randomized and nonrandomized studies. , 1974 .

[2]  D. Rubin Randomization Analysis of Experimental Data: The Fisher Randomization Test Comment , 1980 .

[3]  D. Rubin,et al.  The central role of the propensity score in observational studies for causal effects , 1983 .

[4]  D. Rubin,et al.  Reducing Bias in Observational Studies Using Subclassification on the Propensity Score , 1984 .

[5]  P. Holland Statistics and Causal Inference , 1985 .

[6]  P. Rosenbaum A Characterization of Optimal Designs for Observational Studies , 1991 .

[7]  D B Rubin,et al.  Matching using estimated propensity scores: relating theory to practice. , 1996, Biometrics.

[8]  Peter Sandercock,et al.  The International Stroke Trial (IST): a randomised trial of aspirin, subcutaneous heparin, both, or neither among 19 435 patients with acute ischaemic stroke , 1997, The Lancet.

[9]  G. Imbens The Role of the Propensity Score in Estimating Dose-Response Functions , 1999 .

[10]  E W Steyerberg,et al.  See Blockindiscussions, Blockinstats, Blockinand Blockinauthor Blockinprofiles Blockinfor Blockinthis Blockinpublication Prognostic Blockinmodels Blockinbased Blockinon Blockinliterature Blockinand Individual Blockinpatient Blockindata Blockinin Blockinlogistic Blockinregression Analysis Article Blo , 2022 .

[11]  J. Concato,et al.  Randomized, controlled trials, observational studies, and the hierarchy of research designs. , 2000, The New England journal of medicine.

[12]  B. Hansen Full Matching in an Observational Study of Coaching for the SAT , 2004 .

[13]  Kosuke Imai,et al.  Causal Inference With General Treatment Regimes , 2004 .

[14]  Patrick Royston,et al.  Construction and validation of a prognostic model across several studies, with an application in superficial bladder cancer , 2004, Statistics in medicine.

[15]  Elaine L. Zanutto,et al.  Using Propensity Score Subclassification for Multiple Treatment Doses to Evaluate a National Antidrug Media Campaign , 2005 .

[16]  G. Imbens,et al.  The Propensity Score with Continuous Treatments , 2005 .

[17]  G. Imbens,et al.  On the Failure of the Bootstrap for Matching Estimators , 2006 .

[18]  Gary King,et al.  Matching as Nonparametric Preprocessing for Reducing Model Dependence in Parametric Causal Inference , 2007, Political Analysis.

[19]  B. Hansen The prognostic analogue of the propensity score , 2008 .

[20]  S. Cole,et al.  Invited commentary: positivity in practice. , 2010, American journal of epidemiology.

[21]  Elizabeth A Stuart,et al.  Matching methods for causal inference: A review and a look forward. , 2010, Statistical science : a review journal of the Institute of Mathematical Statistics.

[22]  Til Stürmer,et al.  Confounder summary scores when comparing the effects of multiple drug exposures , 2010, Pharmacoepidemiology and drug safety.

[23]  Tianxi Cai,et al.  Robust Prediction of t‐Year Survival with Data from Multiple Studies , 2011, Biometrics.

[24]  Malcolm Rowland,et al.  Bridging the efficacy–effectiveness gap: a regulator's perspective on addressing variability of drug response , 2011, Nature Reviews Drug Discovery.

[25]  P. Sandercock,et al.  The International Stroke Trial database , 2011, Trials.

[26]  Karel G M Moons,et al.  Aggregating published prediction models with individual participant data: a comparison of different approaches , 2012, Statistics in medicine.

[27]  Sebastian Schneeweiss,et al.  Role of disease risk scores in comparative effectiveness research with emerging therapies , 2012, Pharmacoepidemiology and drug safety.

[28]  Kristin E. Porter,et al.  Diagnosing and responding to violations in the positivity assumption , 2012, Statistical methods in medical research.

[29]  Xiao-Hua Zhou,et al.  Generalized propensity score for estimating the average treatment effect of multiple treatments , 2012, Statistics in medicine.

[30]  Elizabeth A Stuart,et al.  On the joint use of propensity and prognostic scores in estimation of the average treatment effect on the treated: a simulation study , 2014, Statistics in medicine.

[31]  Karel G M Moons,et al.  Meta‐analysis and aggregation of multiple published prediction models , 2014, Statistics in medicine.

[32]  A. Vickers Clinical trials in crisis: Four simple methodologic fixes , 2014, Clinical trials.

[33]  Alan R. Ellis,et al.  Matching on the disease risk score in comparative effectiveness research of new treatments , 2015, Pharmacoepidemiology and drug safety.

[34]  Karel G M Moons,et al.  A new framework to enhance the interpretation of external validation studies of clinical prediction models. , 2015, Journal of clinical epidemiology.

[35]  Elizabeth A. Stuart,et al.  Optimal full matching for survival outcomes: a method that merits more widespread use , 2015, Statistics in medicine.

[36]  Shu Yang,et al.  Propensity score matching and subclassification in observational studies with multi‐level treatments , 2015, Biometrics.

[37]  Sebastian Schneeweiss,et al.  Comparison of high-dimensional confounder summary scores in comparative studies of newly marketed medications. , 2016, Journal of clinical epidemiology.

[38]  Sebastian Schneeweiss,et al.  Dimension reduction and shrinkage methods for high dimensional disease risk scores in historical data , 2016, Emerging Themes in Epidemiology.

[39]  A. Mebazaa,et al.  Propensity score estimators for the average treatment effect and the average treatment effect on the treated may yield very different estimates , 2016, Statistical methods in medical research.

[40]  Alan R. Ellis,et al.  The “Dry-Run” Analysis: A Method for Evaluating Risk Scores for Confounding Control , 2017, American journal of epidemiology.

[41]  S. Schneeweiss,et al.  From Trial to Target Populations - Calibrating Real-World Data. , 2017, The New England journal of medicine.

[42]  Iain Buchan,et al.  Clinical prediction in defined populations: a simulation study investigating when and how to aggregate existing models , 2017, BMC Medical Research Methodology.

[43]  E. Stuart,et al.  Estimating the effect of treatment on binary outcomes using full matching on the propensity score , 2015, Statistical methods in medical research.

[44]  Michael J. Lopez,et al.  Estimation of causal effects with multiple treatments: a review and new ideas , 2017, 1701.05132.

[45]  L. Smeeth,et al.  Propensity score analysis with partially observed covariates: How should multiple imputation be used? , 2017, Statistical methods in medical research.